Smoothing methods role in raw scores Non-linear transformation to Normalized scale scores

Document Type : Original Article


university of tehran psychology and education faculity


In order to the better interpreting and comparing scores in test batteries the raw scores in each test  are converted to a common scale that called scale score. One of the prevalent methods to transform raw scores to scale scores is normalizing. In this research to investigate the role of frequency pre-smoothing and score post-smoothing in normalizing scaling method we used 10000 random simulated sample data and 10000 random real sample data from Iran university entrance exam applicants. The role of smoothing methods in normal scaling method has been analyzed by conditional standard error of measurement that called CSEM, frequency charts and statistical indexes like moments. The results showed that reliability coefficient for all scaling methods are high, but analyzing charts, moments and conditional standard error of measurement illustrated that normalized scale score obtained from the frequencies smoothing method are the more accurate and fewer errors, Furthermore using pre-smoothing lead to reduce score error undulation.  


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